4x^2+5x=400

Simple and best practice solution for 4x^2+5x=400 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2+5x=400 equation:


Simplifying
4x2 + 5x = 400

Reorder the terms:
5x + 4x2 = 400

Solving
5x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 5x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 5x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-100 + 1.25x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 1.25x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 1.25x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 1.25x + x2 = 0 + 100
1.25x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
1.25x + x2 = 100

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 100 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 100 + 0.390625

Combine like terms: 100 + 0.390625 = 100.390625
0.390625 + 1.25x + x2 = 100.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 100.390625

Calculate the square root of the right side: 10.019512214

Break this problem into two subproblems by setting 
(x + 0.625) equal to 10.019512214 and -10.019512214.

Subproblem 1

x + 0.625 = 10.019512214 Simplifying x + 0.625 = 10.019512214 Reorder the terms: 0.625 + x = 10.019512214 Solving 0.625 + x = 10.019512214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 10.019512214 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 10.019512214 + -0.625 x = 10.019512214 + -0.625 Combine like terms: 10.019512214 + -0.625 = 9.394512214 x = 9.394512214 Simplifying x = 9.394512214

Subproblem 2

x + 0.625 = -10.019512214 Simplifying x + 0.625 = -10.019512214 Reorder the terms: 0.625 + x = -10.019512214 Solving 0.625 + x = -10.019512214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -10.019512214 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -10.019512214 + -0.625 x = -10.019512214 + -0.625 Combine like terms: -10.019512214 + -0.625 = -10.644512214 x = -10.644512214 Simplifying x = -10.644512214

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.394512214, -10.644512214}

See similar equations:

| 4x+5=-8+-6 | | 2x-[5x-(6x+2)]=14-x | | 4(2x+3)-8=11x-3(x+2) | | 5000/60 | | 35000.00+1680.00c=300440.00 | | 17y-51=4y+40-13 | | .5a+(a-1)-(.2a+10)=.2a-(.2a-28) | | 7x^2-6x-9=0 | | -13=-14k+k | | 10-(x+6)-2=-5x+9-(-5x+3) | | 7x-4=4x+10 | | 9=20-x | | x^2-5=12 | | 4x*2-24x+100=0 | | (x-5)(5x+3)=0 | | 2x-1-8=18 | | 5v^2+4=-9v | | 18s-17s=10 | | log(-2p+6)=3 | | 13a+13a+3a+14a=-9 | | 7x-(x^2-x-9)=17-x^2 | | 3u+3u=18 | | Lynx=10 | | 14a-9a=10 | | 13x-(x+21)=39 | | 5y(4x-6)=8 | | -5r^6+3r^4-3r^2= | | 2.35/0.5 | | x-3(-4)=14 | | 9x^2-18x+16=8x^2-24x+25 | | 18x+12=9x+45 | | -1.716x^2+1.716x+10=0 |

Equations solver categories